The random variable \(Y\) is the sum of two independent observations of the random variable \(X\). The probability generating function \(\mathrm{G}_{Y}(t)\) of \(Y\) is given by
\(\mathrm{G}_{Y}(t)=\frac{t^{2}}{(4-3 t)^{4}}\)
(a) Find \(E(Y)\).

(b) Write down an expression for the probability generating function of \(X\).

(c) Find \(\mathrm{P}(X=4)\).